The incident, involving a Grey Vauxhall Corsa, happened around 7.10pm on Tuesday, December 3, just off Holehouse Brae in Neilston, near to the junction with Main Street.
The fire was extinguished by the Scottish Fire and Rescue Service and there were no reports of any injuries.
Detective Constable Craig Whyte, of Greater Glasgow CID, said: “Our enquiries into this incident are ongoing and the fire is being treated as wilful.
“I am appealing for anyone who witnessed the incident to contact us.
“I would also ask anyone who was in the area around the time and who may have dash cam or private CCTV footage which could assist to get in touch.”
Anyone with information is asked to contact 101, quoting reference 3163 of the December 3, 2024.
Alternatively, Crimestoppers can be contacted anonymously on 0800 555 111.
